%I #21 Nov 28 2021 13:36:47

%S 1,2,3,8,5,12,7,32,27,20,11,144,13,28,15,256,17,216,19,160,63,44,23

%N a(n) is the minimal order of a group in which all groups of order n can be embedded.

%D Heffernan, Robert, Des MacHale, and Brendan McCann. "Cayley's Theorem Revisited: Embeddings of Small Finite Groups." Mathematics Magazine 91.2 (2018): 103-111.

%H Heffernan, Robert, Des MacHale, and Brendan McCann, <a href="https://arxiv.org/abs/1706.09286">Minimal embeddings of small finite groups</a>, arXiv:1706.09286 [math.GR], Jun 28 2017.

%H MathStackExchange, <a href="https://math.stackexchange.com/questions/4269307/how-powerful-is-cayleys-theorem">How powerful is Cayley's theorem?</a>, Oct 07 2021.

%F From _David A. Craven_, Oct 07 2021: (Start)

%F a(p)=p, a(p^2)=p^3, a(p^3)=p^6 if p is odd, a(8)=32.

%F If p<q are distinct primes, a(pq)=p^2q if p divides (q-1), a(pq)=pq otherwise. (End)

%Y Cf. A000001, A340515.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, Feb 02 2021

%E a(16)-a(23) from _David A. Craven_, Oct 07 2021